Spring 2002–2003

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Characteristic classes are basic topological invariants of manifolds and bundles. They occur naturally in various problems of topology, differential and algebraic geometry, and theoretical physics (e.g., string theory). 

Time permitting, we plan to discuss vector bundles, Euler, Pontrjagin, Chern, Stiefel-Whitney classes, signature, obstruction theory, intersection numbers, cobordisms, K-theory, spin geometry, and Chern-Weil theory.

Text: Characteristic classes by John W. Milnor and James D. Stasheff, Princeton University Press, 1974. The book is on permanent reserve in Millikan. This wonderful book is somewhat dated so we shall be drawing on various other  sources as needed. 

Prerequisite:  Ma 151ab is more than enough.

Grading Policy:  The grade will be determined by occasional homework and class presentation(s) on the subject of the course (typically a section from the text).
     
Contact Info:

• Office: 178 Sloan 
• ibeleg@caltech.edu 
• Office Hours: by appointment (to be made by email)